Well-defined phase of simplicial quantum gravity in four dimensions

Abstract

We analyze simplicial quantum gravity in four dimensions using the Regge approach. The existence of an entropy-dominated phase with a small negative curvature is investigated in detail. It turns out that observables of the system possess finite expectation values although the Einstein-Hilbert action is unbounded. This well-defined phase is found to be stable for a one-parameter family of measures. A preliminary study indicates that the influence of the lattice size on the average curvature is small. We compare our results with those obtained by dynamical triangulation and find qualitative correspondence.